Year: 2020
Author: Qingsong Gu, Hui Rao
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 4 : pp. 457–467
Abstract
In this paper we prove that the critical exponents of Besov spaces on a compact set possessing an Ahlfors regular measure is an invariant under Lipschitz transforms. Under mild conditions, the critical exponent of Besov spaces of certain self-similar sets coincides with the walk dimension, which plays an important role in the analysis on fractals. As an application, we show examples having different critical exponents are not Lipschitz equivalent.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-SU5
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 4 : pp. 457–467
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Lipschitz invariant Besov space critical exponents walk dimension heat kernel.